Verifying formulas for interventional distributions

2026-07-15

AI Summary

This study addresses the problem of verifying whether a given observational formula correctly identifies a target interventional distribution in causal graphical models, going beyond mere identifiability assessment. To this end, it introduces a falsification-driven verification framework that decouples verification from identification for the first time: an efficient falsifier first eliminates incorrect formulas, and a verifier—provably almost surely correct under regular exponential family models—is then constructed atop this filter. As an application, the authors develop a “gateway test” that enumerates all valid variable sets satisfying the front-door criterion, with theoretical guarantees on verification reliability. This approach substantially enhances both the practicality and rigor of validating interventional distributions.

Abstract

We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and use the resulting verifier to develop the gateway test, which finds all sets admissible for use in a front-door formula.

Problem

• causal graphical models
• interventional distribution
• identification
• verification
• observational formula

Innovation

• causal verification
• interventional distribution
• falsifier
• front-door criterion
• exponential-family models